BIO 356 Lab 3: Life-History Analysis
Rafael D’Andrea - Stony Brook University - Spring 2023
In this lab you will learn
Life-history analysis is the study of how species allocate resources to growth, survival, reproduction, and dispersal.
Because of finite resources, these budgetary allocations are subject to tradeoffs with important consequences for evolutionary and ecological dynamics.
Life-history tradeoffs between competitive ability and colonization ability may promote coexistence between plants.
Without such tradeoffs, evolution would give rise to a Darwinian demon.
According to the intermediate disturbance hypothesis, environmental disturbance may promote species diversity up to a point.
library(tidyverse)
library(gridExtra) ## for plotting function grid.arrange()
library(deSolve) ## for ODE model
library(magrittr) ## for pipe symbol %<>%
library(knitr) ## for table-viewing function kable()theme_set(theme_bw())
theme_update(panel.grid = element_blank())
Darwinian Demon: A hypothetical organism that is able to maximize all elements of its fitness simultaneously. It reproduces immediately after birth, produces the maximum number of young, and lives indefinitely. No such organism could exist, but biologists use the concept in thought experiments concerning life history strategies and evolutionary trade-offs. A Dictionary of Ecology 4th ed, Oxford U. Press, 2010
Hypothetical Darwinian Demon: A superplant which grows quickly due to its high efficiency in absorbing and processing light and nutrients, reproduces constantly with a large output of big seeds, and has a long lifespan as it is well-defended against stressors including herbivores, disease, and drought. Figure credit: Cory Warner
Life history analysis is the study of how species allocate resources to different aspects of fitness, including individual growth, reproduction, dispersal, and survival. Typically we are interested in how these allocation strategies affect the schedules of important milestones in the life of an individual. Examples include age-specific fecundity and mortality, stage-specific growth rate, age at first reproduction, number of offspring, size of offspring, longevity, etc.
As we saw in the last module on the growth of structured populations, variation in fecundity and mortality over the course of an individual’s life can have substantial consequences for the growth of the population. Some applications of life history analysis include determining the most critical stages for sustained growth of the population, which in turn is vital information for natural resource managers and conservationists.
Here we will take a deeper look at examples of different life history strategies in animals and plants, focusing on the tradeoffs that constrain and modulate these strategies.
Survival vs reproduction
Reproduction is arguably the ultimate component of fitness, and is therefore under unrelenting pressure from natural selection. The genes of parents that reproduce more and faster will be overrepresented in future generations. If there were no constraints on reproduction, this would quickly lead to organisms that invest all their energy into reproducing constantly from birth until death. Of course this does not happen, for the obvious reason that there are costs to reproduction—including a shorter life!
Figure: Maize, rice, wheat, and sorghum, annual cereals which provide over half of all calories consumed by humans worldwide. Images from Wikipedia (maize, rice, wheat) and University of California (sorghum).
Q1. During the process of domestication, humans replace natural selection as they choose to reproduce individuals with specific traits over successive generations of animals and plants. All domesticated cereals (maize, wheat, rice, sorghum, etc) are annuals (i.e. complete their life cycle in a single year). By contrast, many of their wild relatives in the grass family Poaceae are perennials (ie live longer than one year). How would you make sense of this discrepancy in light of the evolutionary theory of tradeoffs between reproduction and survival?
Another striking example of the effects of domestication on life history traits is the domestic silk moth, Bombyx mori. Silk is produced by the caterpillars as a protective cocoon for the otherwise vulnerable pupal stage of the moth. Domesticated silkworms grow faster and produce bigger silk cocoons than their wild kin, Bombyx mandarina. This higher efficiency of the larval stage and added protection in the pupal stage could increase survival in the wild. However, the species cannot reproduce without human aid, as the female lost the ability to fly and thus find a mate.
Figure: Comparison of the female adults of the domesticated silk moth, B. mori (left) and its wild cousin B. mandarina (right). Comparison of the silk cocoons produced by the respective species. Photos by Markus Knaden, Max Planck Institute for Chemical Ecology.
Note: Domesticated maize also cannot reproduce without humans. The leafy sheath surrounding the cob will not fall open, leaving the kernels trapped inside, and the kernels themselves will not scatter from the cob as they do in maize’s wild ancestor, teosinte.
Ultimately, many domesticated species benefit humans by providing food (cereals, meat, eggs), other goods (textiles, dyes, building materials), or services (plowing, transportation, companionship), while also depending on humans as they cannot survive or reproduce alone or as efficiently as their wild ancestors. Domestication does double duty for students of ecology as it is an example of mutualism with huge consequences to us (we will discuss mutualism in more detail later in the course), and also a vivid demonstration of the inevitable life-history tradeoffs in nature.
The examples above showcase the tradeoff between survival and reproduction, but in nature those tradeoffs can encompass any aspects of fitness, as we will see below.
Q2. Describe another example of domesticated organism not mentioned above or in lecture, where selective breeding for a desirable life-history trait (e.g. growth, reproduction) may have caused a change in another life-history trait (e.g. survival).
Early breeding vs late breeding
The constraints posed by a finite energy budget that must be distributed between reproduction and survival (after all, an organism must be alive in order to reproduce) lead to questions about optimal reproductive schedules— ie, investment in reproducing early vs late in life.
The table below summarizes the results of a lab experiment by Rose and Charlesworth (1981) on fruit flies, Drosophila melanogaster. Over twelve generations, flies from line CB were prevented from reproducing past Day 6 since emerging from the pupal stage (ie only eggs laid by Day 6 of the adult’s life were allowed to contribute to the next CB generation), while flies from line CO were prevented from reproducing before Day 6 (only eggs laid past Day 6 contributed to the next CO generation). After the selection stage was completed, both lines were assayed for their egg-laying schedules.
Figure: Drosophila melanogaster, by Andre Karwath
Table: Comparison of egg laying between D. melanogaster lines selected for early (CB) and late (CO) reproduction. Adapted from Rose and Charlesworth 1981
Q3. Which population evolved a later breeding schedule, CO or CB? Support your answer based on the table.
Q4. Which population evolved longer lifespans? How do you connect this answer with the answer to the previous question, based on life history theory?
Q5. Assuming that longevity and late breeding schedules coevolve as indicated in this experiment, what would you predict regarding the evolved reproductive schedules (late breeder vs early breeder) of a species that lives in an uncertain environment where individuals are prone to unpredictable mortality?
Growth vs survival
One well-known tradeoff for tree species in closed-canopy forests (where light is a limiting resource near the forest floor) is between growth in well-lit environments versus survival in low light. Shade-tolerant species typically grow slowly regardless of the light environment, whereas species that outgrow others in favorable conditions (eg after a clearing in the forest canopy) tend to languish in the shade. (“Growth” here refers to the rate at which a tree gets larger every year, not the growth rate of the species.)
Figure: Bird’s eyeview of Barro Colorado Island, a closed-canopy forest, where most light is absorbed by vegetation before reaching the forest floor except for gaps/clearings left by dead trees. Photo by Chris Ziegler.
For example, Wright et al. Ecology 2010 measured the demographic rates of every tree in a 50-hectare plot in Barro Colorado Island, Panama. They found that saplings (young immature trees) of species characterized by fast annual tree growth have lower chances of survival than saplings of species with slow growth. Specifically, for each species they averaged the relative growth rate (RGR, the yearly diameter gain per centimeter of trunk diameter) of the top 5% fastest-growing saplings and the survival rates of the bottom 25% slowest-growing saplings, and found a strong negative correlation between these rates across species (figure below).
Figure: Survival of slowest growing saplings correlates negatively with relative growth rate of fastest growing saplings in Barro Colorado Island, Panama. Data shown for 103 species. Adapted from Wright et al 2010.
Q6. Why did the authors specifically compare the growth of the fastest-growing saplings against survival of the slowest-growing saplings, as opposed to comparing average growth to average survival across all trees of each species? Hint: one may reasonably assume that the fastest-growing trees of each species are growing in high light, while the slowest-growing individuals are growing in low light.
Species life history strategies are reflected in their functional traits, which are defined as characteristics of an organism’s phenotype that impact its performance Violle et al. 2007. Elements of the phenotype include the organism’s morphology, physiology, phenology, and behavior, while the elements of performance are the organism’s rates of growth, reproduction, dispersal, and survival.
Wood density, measured as the dry mass per volume of woody tissue, is a functional trait for plants. It is associated with structural strength (resistance to breakage and mechanical support) and water storage, but lower sapwood conductivity and higher construction costs Chave et al. 2007.
Q7. If you were to measure the wood density of all species on BCI and compare it to rates of survival and individual growth, would you expect to see a positive or negative association between wood density and survival? What about relative growth rate? Explain your answer.
Wright et al. 2010 report relationships between four functional traits and sapling survival. The four functional traits were
HEIGHT: maximum plant height, in meters. The average height of the six largest trees of each species. Associated with levels of direct insulation at maturity.
LMA: leaf mass per area, in grams per \(m^2\). Mean leaf mass per area determined from leaf discs for the six smallest individuals of each species. Associated with plant investments in leaf longevity and leaf structural strength.
LOGSEEDMASS: logarithm of the mean seed dry mass, in grams. Associated with parental subsidies to the seedlings at early stages of development.
WSG: wood specific gravity (ie wood density), in grams per \(cm^3\). Associated with structural strength and water storage.
The table below lists the correlation coefficient between sapling survival and each of the four traits, as well as the p-value of the correlation test, which indicates whether the observed correlation is significantly different from zero (a reported p-value of 0 indicates that the p-value is \(< 0.001\)).
| trait | Pearson correlation coefficient | p value |
|---|---|---|
| HEIGHT | 0.00 | 0.983 |
| LMA | 0.36 | 0.000 |
| LOGSEEDMASS | 0.39 | 0.001 |
| WSG | 0.48 | 0.000 |
Q8. Did the empirical observations match your prediction for wood density?
Q9. Which of the traits had the weakest correlation with sapling survival? How would you explain this finding?
Q10. Check the correlation between the functional traits and relative growth rate of saplings by running the code below. Describe the plots and explain whether they support or contradict the hypothesis of a growth-survival tradeoff.
dat =
read.table(
'https://raw.githubusercontent.com/rafaeldandrea/BIO-356/master/Supplement_20100505.txt',
skip = 25,
header = TRUE
) %>%
as_tibble
## Original data set records missing data as -99. This line replaces it with NA
dat[dat == -99] = NA
dtf =
dat %>%
select(GENUS., SPECIES., WSG, SEEDMASS, HEIGHT, LMA, RGR95SAP, MRT25SAP) %>%
mutate(LOGSEEDMASS = log10(SEEDMASS)) %>%
pivot_longer(-c(GENUS., SPECIES., RGR95SAP, MRT25SAP), names_to = 'trait') %>%
mutate(growth = RGR95SAP, survival = 100 - MRT25SAP) %>%
select(-c(RGR95SAP, MRT25SAP)) %>%
pivot_longer(c(growth, survival), names_to = 'demographic',values_to = 'rate') %>%
filter(trait != 'SEEDMASS')
plot_growth_vs_traits =
dtf %>%
filter(demographic == 'growth') %>%
ggplot(aes(value, rate)) +
geom_point() +
theme(aspect.ratio = 1) +
facet_wrap(~ trait, ncol = 2, scales = 'free') +
labs(
x = 'trait value',
y = 'relative growth rate of fastest-growing saplings (cm per cm dbh per year)'
) +
ggtitle('Sapling growth rate vs functional traits on BCI')
plot_growth_vs_traits
Competition vs colonization
As you walk through a forest, notice how the forest floor is covered in small seedlings. Only a fraction of these seedlings ever recruit into later life stages (sapling, young adult, mature tree), because of intense competition with other seedlings for space and nutrients. This gives rise to a slew of potential life-history strategies for succeeding in the competition for space among plants.
Figure: A northern hardwood stand in Michigan. Notice the carpet of seedlings on the forest floor. Only a small fraction of those seedlings ultimately recruits into sapling and adult stage, implying strong competition for recruitment among seedlings. From US Forest Service, USDA
The competition-colonization tradeoff Levins and Culver 1971 is a hypothetical budgetary tradeoff between allocation to reproduction/dispersal (colonization) and survival (competition). Species on the colonization end of the spectrum have high fecundity but low seedling survival, and thus low ability to compete for seedling recruitment. Species on the competition end of the spectrum have traits that allow them to compete strongly for recruitment against other germinating seeds, at the cost of being slow to reproduce and/or disperse. This could occur, for example, because of a tradeoff between seed size and seed output:
Some species may invest in producing many small easy-to-disperse seeds, such that their seeds are the first to arrive and germinate at a new gap in the forest (i.e. high colonization ability). If the site is uncontested by other species, those species will dominate.
In contrast, other species may invest in large high-quality (and costly to produce) seeds, thus making sure that their seedlings will be the ones to recruit in the sites that they do colonize by displacing previously germinated seedlings of weaker species (high competitive ability).
Figure: Diagram representing one manifestation of the competition-colonzation tradeoff. Small-seeded species can produce many seeds. Large-seeded species can only produce relatively few seeds, but those high-quality seeds have better chances of beating other species in competition for recruitment. From D’Andrea et al. PLoS Comp Bio 2019
Mathematically, we can write the model for \(S\) species in a community as follows:
\[ \frac{1}{p_i}\frac{dp_i}{dt} = f_i\left(1-\sum_{j=1}^S p_j\right) + \sum_{j=1}^S (f_iH_{ij} - f_j H_{ji}) \, p_j - m_i \] where \(p_i\), \(f_i\), amd \(m_i\) are the occupancy (proportion of sites occupied by the species), fecundity (seed output), and mortality rate of species \(i\), and \(H_{ij}\) is the probability that a seedling of species \(i\) beats a seedling of species \(j\) for recruitment at a site. In words, the model is saying that species abundances decrease due to mortality and increase due to recruitment. Species will recruit in empty sites in proportion to their fecundities. They can also recruit in occupied sites by displacing the current occupant, and they can in turn be displaced by other species. Displacement is mediated by the species competitive ability as encoded in the coefficients \(H_{ij}\).
The following R code implements the model.
## Model
CCT_Model =
function(
initial_p,
fecundity,
mortality,
displacement_matrix,
final_time,
time_step
){
CCT =
function(t, state, parameters){
with(as.list(parameters), {
p = state
p[p < 1e-200] = 0
dpdt =
((1 - sum(p)) * f - m + as.numeric(T %*% p)) * p
list(dpdt)
})
}
times = seq(0, final_time, by = time_step)
parameters =
list(
f = fecundity,
m = mortality,
h = displacement_matrix,
T = fecundity * displacement_matrix - t(fecundity * displacement_matrix)
)
state = initial_p
out = ode(y = state, times = times, func = CCT, parms = parameters)
out[out < 0] = 0
return(
list(
parameters =
list(
initial_p,
fecundity,
mortality,
displacement_matrix
),
initial_conditions = initial_p,
state = out
)
)
}
# Plotting the model outcome
Plot_CCT_timeseries =
function(model){
as.data.frame(model$state) %>%
pivot_longer(-time, names_to = 'species', values_to = 'occupancy') %>%
ggplot(aes(time, occupancy, group = species, color = species)) +
geom_line(size = 1) +
expand_limits(y = 0)
}
Plot_CCT_stemplot =
function(trait, model){
tibble(trait = trait, occupancy = model$state[nrow(model$state), -1]) %>%
ggplot() +
geom_segment(aes(trait, occupancy, xend = trait, yend = occupancy - occupancy)) +
geom_point(aes(trait, occupancy))
}The simplest way to implement the competition-colonization tradeoff is to assume that lower-fecundity species always displace higher-fecundity species. In that case, if we line up our species in order of fecundity \(f_1 < f_2 < f_3\) etc, then \(H_{ij} > 1\) if \(i < j\) and zero otherwise.
Let’s use this idea and see if two species can coexist based on this tradeoff. We’ll set the fecundity of species A to 1 seed per unit time, and species B to 5 seeds per unit time. For simplicity we will assume equal mortality to both species, \(m = 0.7\) deaths per individual per unit time.
# Parameters
number_of_species = 2
fecundity = c(1, 5)
p0 = c(.1, .1)
mortality = .7
final_year = 25
# Call the model
model =
CCT_Model(
initial_p = p0,
fecundity = fecundity,
mortality = mortality,
displacement_matrix = 1 * upper.tri(diag(number_of_species)),
final_time = final_year,
time_step = .1
)
# Plot results
plot_timeseries =
as.data.frame(model$state) %>%
as_tibble %>%
rename(`species A` = `1`, `species B` = `2`) %>%
mutate(empty = 1 - `species A` - `species B`) %>%
pivot_longer(-time, names_to = 'species', values_to = 'occupancy') %>%
ggplot(aes(time, occupancy, group = species, color = species)) +
geom_line(size = 1) +
expand_limits(y = 0) +
theme(aspect.ratio = 1)## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.plot_timeseries
They can!
These two species represent a reproduction specialist (colonizer) with high fecundity and low competitive ability, and a competition specialist (competitor) with low fecundity and high competitive ability due to higher seedling survival. These are two different ecological strategies based on different life history budgets.
Q11. Which species, A or B, is the colonizer and which is the competitor?
According to the model, the competitor always displaces the colonizer wherever they both compete for the same site, but the colonizer isn’t excluded from the community because its higher seed count allows it to frequently be the first to colonize empty sites, of which there is a steady supply every year due to adult mortality.
Q12. Which species should benefit if we decrease adult mortality? Explain your hypothesis, then test it by running the model with reduced mortality \(m = 0.5\). Show your plot.
The competition-colonization tradeoff is one of the classic theoretical explanations for coexistence in plant communities. (We will talk a lot more about coexistence in the Competition module later in the course.) To illustrate how the tradeoff presents species with alternative strategies based on budgeting their life history traits, let’s try the model with 100 species, running the gamut from competition specialists on the left to reproduction specialists on the right and everything in between.
# Parameters
number_of_species = 100
fecundity = seq(81, 1000, length = number_of_species)
p0 = rep(1/number_of_species, number_of_species)
mortality = 80
final_year = 10000
# Call the model
model =
CCT_Model(
initial_p = p0,
fecundity = fecundity,
mortality = mortality,
displacement_matrix = 1 * upper.tri(diag(number_of_species)),
final_time = final_year,
time_step = 1
)
# Plot results
plot_stemplot =
Plot_CCT_stemplot(trait = seq(number_of_species), model = model) +
scale_y_sqrt()
plot_stemplot +
xlab('competition rank')
The plot above shows the long-term occupancy of each species, which are arranged by their competition rank (higher ranked species to the left). Notice that of the 100 starting species, roughly half of them survived and can coexist by adopting different strategies along this axis of competition-vs-reproduction life history budgets. In the end we see an equilibrium of species that thrive by being the first to arrive on the scene when a new vacancy opens up versus species that specialize on competitively dominating the sites they do manage to disperse into. Hence the term competition-colonization tradeoff.
Q13. In the plot above, which species has higher fecundity, species 10 or species 90?
Q14. What would happen if we gave all species the same fecundity? Explain your hypothesis and confirm it by running the model above and replacing the fecundity parameter with a constant.
Q15: How would you connect the theoretical scenario in Q14 to the concept of a Darwinian demon defined at the top of the lab write-up?
Note: There seems to be a neat relationship between occupancy and competitive rank. This is however specific to our particular choice of parameters. The take-home message here is that the tradeoff between competitive ability and colonization ability opens up the possibility of alternative budgeting strategies for plants. We will revisit the competition-colonization tradeoff later in the course. Stay tuned.
Survival versus colonization: the Intermediate Disturbance Hypothesis
As we have seen, under the competition-colonization tradeoff some species specialize in colonizing empty sites while other species invest in displacing others when they finally arrive. As long as there is a steady but not overwhelming supply of newly vacant sites caused by natural mortality, this allows for coexistence between colonizers—the first to arrive at the new sites—and competitors—which eventually displace the colonizers until they themselves die of natural causes, restarting the cycle.
However, if mortality is too low (eg for organisms with long lifespans such as trees), competitors would eventually dominate, and colonizers would be driven out. Conversely, if mortality is too high (eg in frequently disturbed habitats), then colonizers would vanquish competitors, because there just wouldn’t be enough time between disturbance events for the competitors to establish.
These ideas led to the so-called intermediate disturbance hypothesis (IDH). The idea is that species diversity is highest in habitats subject to environmental disturbance causing intermediate mortality levels, because under those circumstances both competitors and colonizers do well.
England et al. 2008 studied macroalgal communities in coral reefs off the coast of Western Australia. They sampled alga from 0.25 \(m^2\) quadrats at sites subject to different levels of wave exposure, which can lead to damage and loss of plant biomass.
Figure: Macroalgal communities in Jurien Bay, Western Australia, subject to different levels of wave exposure. Photos by WA’s Department of Parks and Wildlife.
Plotting species count in the quadrats against degree of wave exposure, they found the following relationship:
Figure: Species count (S) for each quadrat v. cumulative exposure (U) with the regression of best fit (quadratic). From England et al. 2008
Q16. a) Do the results of England et al support the IDH? b) What additional evidence regarding the species examined in the study would further corroborate the IDH?